Deep-learning density functional perturbation theory

Calculating materials’ response to external perturbations — such as electron-phonon coupling — is essential for understanding superconductivity and transport, yet traditional density functional perturbation theory (DFPT) is computationally prohibitive for large systems. We showed that neural networks can emulate DFPT by combining deep-learning DFT Hamiltonians with automatic differentiation, achieving up to three orders of magnitude speedup while preserving ab initio accuracy. This work unifies ground-state DFT and DFPT under a single deep-learning framework.